Biomedical subjects

Matthew B Kennel

Publications and source records attributed to Matthew B Kennel.

9 recordsLinked to original sources

PubMed2006

Variance estimators for the Lempel-Ziv entropy rate estimator.

Lempel and Ziv's 1976 algorithm provides an easy-to-compute way to automatically estimate the entropy rate for symbolic time series, requiring no free parameters. Here we derive an analytical variance estimate for the Lempel-Ziv entropy rate estimator that is easily computable from observations with negligible extra effort beyond the entropy rate itself, and compare to another procedure, a time-series-based bootstrap method. These provide a justified "error bar" quantifying the size of expected fluctuations on the estimate itself, given by the single time series of symbols.

Journal Article↗

PubMed2005

Complete and flexible replacement of chaotic uncertainty with transmitted information.

Natural chaos can be described as an information source emitting symbolic sequences with positive entropy. We use two algorithmic techniques from data compression in a nonstandard way along with a control scheme to replace the natural uncertainty in chaotic systems with an arbitrary digital message. Unlike previous targeting-based control, the controlled, deterministic, transmission appears statistically identical to natural chaos, with a message modulated on it at the intrinsic Kolmogorov-Sinai information generation rate of the chaotic oscillator. Thus, chaotic communication by targeting need not consume any additional channel capacity beyond that required by the message itself and the message-bearing signal may appear identical to the uncontrolled oscillator. We also demonstrate control and data transmission at the channel capacity of the oscillator, the maximum possible data rate compatible with the grammar.

Journal Article↗

PubMed2005

Statistically relaxing to generating partitions for observed time-series data.

We introduce a relaxation algorithm to estimate approximations to generating partitions for observed dynamical time series. Generating partitions preserve dynamical information of a deterministic map in the symbolic representation. Our method optimizes an essential property of a generating partition: avoiding topological degeneracies. We construct an energy-like functional and use a nonequilibrium stochastic minimization algorithm to search through configuration space for the best assignment of symbols to observed data. As each observed point may be assigned a symbol, the partitions are not constrained to an arbitrary parametrization. We further show how to select particular generating partition solutions which also code low-order unstable periodic orbits in a given way, hence being able to enumerate through a number of potential generating partition solutions.

Journal Article↗

PubMed2005

Estimating entropy rates with Bayesian confidence intervals.

The entropy rate quantifies the amount of uncertainty or disorder produced by any dynamical system. In a spiking neuron, this uncertainty translates into the amount of information potentially encoded and thus the subject of intense theoretical and experimental investigation. Estimating this quantity in observed, experimental data is difficult and requires a judicious selection of probabilistic models, balancing between two opposing biases. We use a model weighting principle originally developed for lossless data compression, following the minimum description length principle. This weighting yields a direct estimator of the entropy rate, which, compared to existing methods, exhibits significantly less bias and converges faster in simulation. With Monte Carlo techinques, we estimate a Bayesian confidence interval for the entropy rate. In related work, we apply these ideas to estimate the information rates between sensory stimuli and neural responses in experimental data (Shlens, Kennel, Abarbanel, & Chichilnisky, in preparation).

Bayes Theorem↗

PubMed2004

Testing time symmetry in time series using data compression dictionaries.

Time symmetry, often called statistical time reversibility, in a dynamical process means that any segment of time-series output has the same probability of occurrence in the process as its time reversal. A technique, based on symbolic dynamics, is proposed to distinguish such symmetrical processes from asymmetrical ones, given a time-series observation of the otherwise unknown process. Because linear stochastic Gaussian processes, and static nonlinear transformations of them, are statistically reversible, but nonlinear dynamics such as dissipative chaos are usually statistically irreversible, a test will separate large classes of hypotheses for the data. A general-purpose and robust statistical test procedure requires adapting to arbitrary dynamics which may have significant time correlation of undetermined form. Given a symbolization of the observed time series, the technology behind adaptive dictionary data compression algorithms offers a suitable estimate of reversibility, as well as a statistical likelihood test. The data compression methods create approximately independent segments permitting a simple and direct null test without resampling or surrogate data. We demonstrate the results on various time-series-reversible and irreversible systems.

Journal Article↗

PubMed2004

Hemodynamic observations on a yogic breathing technique claimed to help eliminate and prevent heart attacks: a pilot study.

OBJECTIVE: This pilot study investigated the hemodynamics of a yogic breathing technique claimed "to help eliminate and prevent heart attacks due to abnormal electrical events to the heart," and to generally "enhance performance of the central nervous system (CNS) and to help eliminate the effects of traumatic shock and stress to the CNS." DESIGN: Parameters for (4) subjects were recorded during a preexercise resting period, a 31-minute exercise period, and a postexercise resting period. SETTINGS/LOCATION: Parameters for subjects were recorded in a laboratory at the University of California, San Diego. SUBJECTS: Parameters for 3 males (ages 44, 45, 67) and 1 female (age 41) were recorded. One (1) subject (male age 45) had extensive training in this technique. INTERVENTIONS: This yogic technique is a 1 breath per minute (BPM) respiratory exercise with slow inspiration for 20 seconds, breath retention for 20 seconds, and slow expiration for 20 seconds, for 31 consecutive minutes. OUTCOME MEASURES: Fourteen beat-to-beat parameters were measured noninvasively and calculated for body surface area to yield: stroke index (SI), heart rate (HR), cardiac index, end diastolic index, peak flow, ejection fraction, thoracic fluid index, index of contractility, ejection ratio, systolic time ratio, acceleration index, and systolic, diastolic, and mean arterial pressures (MAPs). Left stroke work index (LSWI) and stroke systemic vascular resistance index (SSVRI) were calculated. RESULTS: We report on SI, HR, MAP, LSWI, and SSVRI and how they can help to describe hemodynamicstate changes. This technique induces dramatic shifts in all hemodynamic variables during the 1 BPM exercise and can produce unique changes in the postexercise resting period after long-term practice that appears to have a unique effect on the brain stem cardiorespiratory center regulating the Mayer wave (0.1-0.01 Hz) patterns of the cardiovascular system. CONCLUSIONS: Preclinical studies are warranted to examine the possible long-term effects of this technique that appear to reset a cardiorespiratory brain-stem pacemaker. We postulate that this effect may be the basis for the purported yogic health claim.

Adult↗

PubMed2003

Estimating good discrete partitions from observed data: symbolic false nearest neighbors.

A symbolic analysis of observed time series requires a discrete partition of a continuous state space containing the dynamics. A particular kind of partition, called "generating," preserves all deterministic dynamical information in the symbolic representation, but such partitions are not obvious beyond one dimension. Existing methods to find them require significant knowledge of the dynamical evolution operator. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition, avoiding topological degeneracies, by minimizing the number of "symbolic false nearest neighbors." It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible.

Journal Article↗

PubMed2002

Context-tree modeling of observed symbolic dynamics.

Modern techniques invented for data compression provide efficient automated algorithms for the modeling of the observed symbolic dynamics. We demonstrate the relationship between coding and modeling, motivating the well-known minimum description length (MDL) principle, and give concrete demonstrations of the "context-tree weighting" and "context-tree maximizing" algorithms. The predictive modeling technique obviates many of the technical difficulties traditionally associated with the correct MDL analyses. These symbolic models, representing the symbol generating process as a finite-state automaton with probabilistic emission probabilities, provide excellent and reliable entropy estimations. The resimulations of estimated tree models satisfying the MDL model-selection criterion are faithful to the original in a number of measures. The modeling suggests that the automated context-tree model construction could replace fixed-order word lengths in many traditional forms of empirical symbolic analysis of the data. We provide an explicit pseudocode for implementation of the context-tree weighting and maximizing algorithms, as well as for the conversion to an equivalent Markov chain.

Journal Article↗

PubMed2002

False neighbors and false strands: a reliable minimum embedding dimension algorithm.

The time-delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. We demonstrate a reliable method to estimate the minimum necessary embedding dimension that improves upon previous methods by correcting for systematic effects due to temporal oversampling, autocorrelation, and changing time lag. The method gives a sharp and reliable indication of the proper dimension. With little computational cost, the method also distinguish easily between infinite-dimensional colored noise-including noisy periodicity-and low-dimensional dynamics.

Journal Article↗